Show that ||T(x)|| = ||x||, Vx E R². Show that T(x) · T(y) = x · y, Vx € R². Interpret the property (a) in terms of geometry.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Linear Algebra.

Consider a linear transformation T(x)
Ax : R? → R?
where
cos(0) – sin()
sin(0) cos(0)
COS
A :
(а)
(b)
(c)
Show that ||T(x)|| = ||x||, Vx E R².
Show that T(x) · T(y)=x·y, Vx E R?.
Interpret the property (a) in terms of geometry.
=X•Y,
Transcribed Image Text:Consider a linear transformation T(x) Ax : R? → R? where cos(0) – sin() sin(0) cos(0) COS A : (а) (b) (c) Show that ||T(x)|| = ||x||, Vx E R². Show that T(x) · T(y)=x·y, Vx E R?. Interpret the property (a) in terms of geometry. =X•Y,
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